Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
382 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #31774263 | C2 | semidirect |
| 3. #31774245 | C2 | semidirect |
| 4. #31774194 | C2 | semidirect |
| 5. #31774174 | C2 | semidirect |
| 6. #31774097 | C2 | semidirect |
| 7. #31774097 | C2 | semidirect |
| 8. #31774028 | C2 | semidirect |
| 9. #31773995 | C2 | semidirect |
| 10. C4×#16864641 | C2 | semidirect |
| 11. #557×C271 | C2 | semidirect |
| 93. Q8×C271 | #41 | semidirect |
| 124. C271 | #3368 | semidirect |
| 126. #557 | D271 | semidirect |
| 204. Q8 | #16864655 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774569 | 2 |
| #31774263 | 2 |
| #31774245 | 2 |
| #31774194 | 2 |
| #31774174 | 2 |
| #31774097 | 2 |
| #31774028 | 2 |
| #31773995 | 2 |
| C4×#16864641 | 2 |
| #557×C271 | 2 |
| #3368 | 271 |